Delay-Dependent Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Switched Delay Systems

This paper investigates the problem of delay-dependent output feedback guaranteed cost controller design for uncertain discrete-time switched systems with time-varying state delay. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a switched dynamic output feedback controller guaranteeing the asymptotic stability of the resulting closed-loop system and minimizing a specified cost function. Based on a delay-dependent switched Lyapunov-Krasovskii functional (DDSLKF) combined with Finsler´s Lemma, a novel delay-dependent robust performance analysis result is first proposed and in turn the output feedback controller synthesis is developed. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.